Infrared analysis of the tridimensional Gross-Neveu model: pointwise bounds for the effective potential

Aldo Procacci; Emmanuel Pereira

Annales de l'I.H.P. Physique théorique (1999)

  • Volume: 71, Issue: 2, page 129-198
  • ISSN: 0246-0211

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Procacci, Aldo, and Pereira, Emmanuel. "Infrared analysis of the tridimensional Gross-Neveu model: pointwise bounds for the effective potential." Annales de l'I.H.P. Physique théorique 71.2 (1999): 129-198. <http://eudml.org/doc/76833>.

@article{Procacci1999,
author = {Procacci, Aldo, Pereira, Emmanuel},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {renormalization group; fermionic systems; tree expansion technique; smooth ultraviolet cut-off; convergent perturbative expansion},
language = {eng},
number = {2},
pages = {129-198},
publisher = {Gauthier-Villars},
title = {Infrared analysis of the tridimensional Gross-Neveu model: pointwise bounds for the effective potential},
url = {http://eudml.org/doc/76833},
volume = {71},
year = {1999},
}

TY - JOUR
AU - Procacci, Aldo
AU - Pereira, Emmanuel
TI - Infrared analysis of the tridimensional Gross-Neveu model: pointwise bounds for the effective potential
JO - Annales de l'I.H.P. Physique théorique
PY - 1999
PB - Gauthier-Villars
VL - 71
IS - 2
SP - 129
EP - 198
LA - eng
KW - renormalization group; fermionic systems; tree expansion technique; smooth ultraviolet cut-off; convergent perturbative expansion
UR - http://eudml.org/doc/76833
ER -

References

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  1. [1] Abdesselam and V. Rivasseau, Explicit fermionic tree expansions, Lett. Math. Phys.44 (1) (1998) 77-88. Zbl0907.60087MR1623695
  2. [2] G.A. Battle and P. Federbush, A phase cell cluster expansion for euclidean field theory, Ann. Phys.142 (1982) 95-139. MR674356
  3. [3] G. Benfatto and G. Gallavotti, Perturbation theory of the Fermi surface in a quantum liquid, J. Stat. Phys.59 (3-4) (1990) 541-664. Zbl0716.76090MR1063175
  4. [4] G. Benfatto and G. Gallavotti, Renormalization Group, Princeton University Press, Princeton, NJ, 1995. Zbl0830.58038MR1380265
  5. [5] G. Benfatto, G. Gallavotti and V. Mastropietro, Renormalization group and the Fermi surface in the Luttinger model, Phys. Rev. B45 (1992) 5468. 
  6. [6] G. Benfatto, G. Gallavotti, A. Procacci and B. Scoppola, Beta function and Schwinger functions for a many fermions system in one dimension, Anomaly of the Fermi surface, Commun. Math. Phys.160 (1994) 91-171. Zbl0808.35112MR1262193
  7. [7] D. Brydges, A Short Course on Cluster Expansion, Les Houches1984, K. Osterwalder and R. Stora (Eds.), North-Holland, 1986. MR880525
  8. [8] D. Brydges and H.-T. Yau, Grad φ perturbations of massless Gaussian fields, Commun. Math. Phys.129 (1990) 351-392. Zbl0705.60101MR1048698
  9. [9] M. Disertori and V. Rivasseau, Continuos constructive fermionic renormalization, Preprint (1998). MR1756290
  10. [10] P.A. Faria Da Veiga, Construction de modéles non renormalisables en théorie quantique des champs, Thesis, Ecole Polytechnique, 1991. 
  11. [11] J. Feldman, J. Magnen, V. Rivasseau and R. Seneor, A renormalizable field theory: the massive Gross-Neveu model in two dimensions, Commun. Math. Phys.103 (1986) 67-103. Zbl0594.58060MR826858
  12. [12] G. Gallavotti, Renormalization Group, Troisième cycle de la Physique, Lausanne, 1990. 
  13. [13] G. Gallavotti, Renormalization theory and ultraviolet stability for scalar fields via renormalization group methods, Rev. Mod. Phys.57 (1985) 471-562. MR789582
  14. [14] K. Gawedzki and A. Kupiainen, Block spin renormalization group for dipole gas and (∇φ)4, Ann. Phys.147 (1983) 198-243. MR707525
  15. [15] K. Gawedzki and A. Kupiainen, Gross-Neveu model through convergent perturbation expansions, Commun. Math. Phys.102 (1985) 1-30. MR817285
  16. [16] C. Kopper, J. Magnen and V. Rivasseau, Mass generation in a large N Gross-Neveu model, Commun. Math. Phys.169 (1995) 121-180. Zbl0824.46090MR1328264
  17. [17] D. Iagolnitzer and J. Magnen, Asymptotic completeness and multiparticle structure in field theories. II Theories with renormalization: the Gross-Neveu model, Commun. Math. Phys.111 (1987) 81-100. MR896761
  18. [18] A. Lesniewski, Effective action for the Yukawa 2 quantum field Theory, Commun. Math. Phys.108 (1987) 437-467. MR874903
  19. [19] M. O'Carroll and E. Pereira, A representation for the generating and correlation functions in the block field renormalization group formalism and asymptotic freedom, Ann. Phys.218 (1992) 139-159. Zbl0875.47004MR1179925
  20. [20] E. Pereira, Orthogonality between scales in a renormalization group for fermions, J. Stat. Phys.78 (3-4) (1995) 1067-1082. Zbl1102.82313
  21. [21] E. Pereira and M. O'Carroll, Orthogonality between scales and wavelets in a representation for correlation functions. The lattice dipole gas and (∇φ)4 models, J. Stat. Phys.73 (3-4) (1993) 695-721. MR1251660
  22. [22] E. Pereira and M. Procacci, Block renormalization group in a formalism with lattice wavelets: correlation function formulas for interacting fermions, Ann. Phys.255 (1) (1997) 19-33. Zbl0926.46064MR1436053
  23. [23] E. Pereira, A. Procacci and M. O'Carroll, Multiscale formalism for correlation functions of fermions. Infrared analysis of the tridimensional Gross-Neveu model, J. Stat. Phys.95 (3/4) (1999) 669-696. Zbl1156.81427MR1700930
  24. [24] D. Ruelle, Statistical Mechanics, Rigorous Results, W.A. Benjamin, New York, 1969. Zbl0177.57301MR289084

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